Effective crosstalk estimation in presence of clipping errors

ABSTRACT

A method of reducing crosstalk into a victim line from disturber lines in a communication system may include obtaining a pilot matrix and a measurement vector associated with the pilot matrix, the pilot matrix representing pilot signals transmitted by at least the disturber lines, the measurement vector being influenced by the pilot signals via the crosstalk; estimating estimated crosstalk coefficients of significant ones of the disturber lines by solving a reduced linear system using only non-clipped measurements in the measurement vector, the reduced linear system being derived from the pilot matrix; determining compensation coefficients to reduce the crosstalk based on the estimated crosstalk coefficients; and reducing crosstalk by one or more of pre-compensating signals transmitted on the victim line and post-compensating signals received on the victim line based on the compensation coefficients.

BACKGROUND

1. Field

Example embodiments relate generally to an apparatus configured toestimate crosstalk coefficients in a communication system and/or reducecrosstalk into a victim line from disturber lines in the communicationsystem based on the estimated crosstalk coefficients, a method and/or anon-transitory computer readable medium configured to perform same.

2. Related Art

Performance of a digital subscriber line (DSL) in terms of capacity maydepend on a number of factors such as attenuation and a noiseenvironment. Performance of a DSL transmission system may be impacted bycrosstalk interference from one twisted line pair to another twistedline pair with the same binder and, to a lesser extent, twisted linepairs in neighboring binders.

Consequently, crosstalk interference may affect data rates across anumber of twisted pair lines.

For instance two communication lines such as two VDSL2 lines which arecollocated next to each other induce a signal in each other. Due to theinduced crosstalk and noise from other sources in the surroundings ofthe communication line, the data transported on these lines may beaffected or corrupted by the crosstalk and noise. By reducing thecrosstalk induced on a communication line or compensating the crosstalkinduced on a communication line, the amount of corrupted data may bereduced and the rate at which information can be reliably communicatedis increased.

Each communication line is a possible disturber line which inducescrosstalk in one or more victim lines. Moreover, in today's systems, thenumber of active communication lines may vary. Thus, the inducedcrosstalk varies as the number of active communication lines vary.

When a communication line joins, an initialization process establishes acommunication session over a given line. Typically, the initializationprocess occurs when a number of other lines are already carrying activecommunication sessions.

In order for the new communication session to start with a maximum ratepossible, the access node may determine the coefficients of crosstalkchannels from active lines into the new joining line. The access nodemay determine these crosstalk coefficients by sending pilot signals onall lines, and observing the resulting received signal at the receiverof the new line.

G.vector uses mutually orthogonal pilots and correlation as described in“Self-FEXT cancellation (vectoring) for use with VDSL2 transceivers,”Series G: Transmission Systems and Media, Digital Systems and Networks,ITU G.993.5, April 2010, the entire contents of which is incorporated byreference.

SUMMARY

One or more example embodiments relate to a method of reducing crosstalkinto a victim line from disturber lines in a communication system.

In some example embodiments, the method includes obtaining a pilotmatrix and a measurement vector associated with the pilot matrix, thepilot matrix representing pilot signals transmitted by at least thedisturber lines, the measurement vector being influenced by the pilotsignals via the crosstalk; estimating estimated crosstalk coefficientsof significant ones of the disturber lines by solving a reduced linearsystem using only non-clipped measurements in the measurement vector,the reduced linear system being derived from the pilot matrix;determining compensation coefficients to reduce the crosstalk based onthe estimated crosstalk coefficients; and reducing crosstalk by one ormore of pre-compensating signals transmitted on the victim line andpost-compensating signals received on the victim line based on thecompensation coefficients.

In some example embodiments, the method includes determining whichelements of the measurement vector are clipped measurements and which ofthe elements are the non-clipped measurements; and determining which ofthe disturber lines are insignificant disturber lines and significantdisturber lines, wherein the estimating includes setting the estimatedcrosstalk coefficients associated with the insignificant disturber linesto zero.

In some example embodiments, the estimating includes determining reducedpilot matrices; and estimating the estimated crosstalk coefficients bysolving a least squares problem based on the reduced pilot matrices.

In some example embodiments, the method includes the solving the leastsquares problem includes computing pseudo-inverse matrices; andmultiplying the non-clipped measurements by the pseudo-inverse matricesto generate the estimated crosstalk coefficients.

In some example embodiments, the estimating includes applying the pilotmatrix to initial sparse ones of the estimated crosstalk coefficients togenerate predicted measurement values; overwriting clipped measurementvalues with the predicted measurement values to generate correctedmeasurement values; multiplying the corrected measurement values by atranspose of the pilot matrix to generate dense ones of the estimatedcrosstalk coefficients; and overwriting ones of the dense ones of theestimated crosstalk coefficients associated with the insignificantdisturber lines to zero to obtain improved sparse ones of the estimatedcrosstalk coefficients.

In some example embodiments, the method includes determining the initialsparse ones of the estimated crosstalk coefficients for one of aplurality of tones based on extrapolating or interpolating the improvedsparse ones of the estimated crosstalk coefficients associated withother tones of the plurality of tones.

In some example embodiments, the other tones of the plurality of tonesare tones having a lower frequency than the one of the plurality oftones.

In some example embodiments, the estimating includes iterativelyimproving the estimated crosstalk coefficients until a stop condition issatisfied.

In some example embodiments, the estimating determines that the stopcondition is satisfied when the estimated crosstalk coefficients for acurrent iteration is sufficiently close to the estimated crosstalkcoefficients for a previous iteration.

In some example embodiments, the obtaining obtains the pilot matrix suchthat columns of the pilot matrix represent columns of a Fourier matrixor Walsh-Hadamard Matrix.

One or more example embodiments relate to a device.

In some example embodiments, the device includes one or more processorsconfigured to reduce crosstalk into a victim line from disturber linesin a communication system by, obtaining a pilot matrix and a measurementvector associated with the pilot matrix, the pilot matrix representingpilot signals transmitted by at least the disturber lines, themeasurement vector being influenced by the pilot signals via thecrosstalk, estimating estimated crosstalk coefficients of significantones of the disturber lines by solving a reduced linear system usingonly non-clipped measurements in the measurement vector, the reducedlinear system being derived from the pilot matrix, determiningcompensation coefficients to reduce the crosstalk based on the estimatedcrosstalk coefficients, and reducing crosstalk by one or more ofpre-compensating signals transmitted on the victim line andpost-compensating signals received on the victim line based on thecompensation coefficients.

In some example embodiments, the one or more processors are furtherconfigured to, determine which elements of the measurement vector areclipped measurements and which of the elements are the non-clippedmeasurements; and determine which of the disturber lines areinsignificant disturber lines and significant disturber lines, whereinthe one or more processors are configured to estimate the estimatedcrosstalk coefficients of significant ones of the disturber lines bysetting the estimated crosstalk coefficients associated with theinsignificant disturber lines to zero.

In some example embodiments, the one or more processors are configuredto estimate the estimated crosstalk values of significant ones of thedisturber lines by, determining reduced pilot matrices; and estimatingthe estimated crosstalk coefficients by solving a least squares problembased on the reduced pilot matrices.

In some example embodiments, the one or more processors are configuredto estimate the estimated crosstalk values of significant ones of thedisturber lines by, applying the pilot matrix to initial sparse ones ofthe estimated crosstalk coefficients to generate predicted measurementvalues; overwriting clipped measurement values with the predictedmeasurement values to generate corrected measurement values; multiplyingthe corrected measurement values by a transpose of the pilot matrix togenerate dense ones of the estimated crosstalk coefficients; andoverwriting ones of the dense ones of the estimated crosstalkcoefficients associated with the insignificant disturber lines to zeroto obtain improved sparse ones of the estimated crosstalk coefficients.

In some example embodiments, the one or more processors are furtherconfigured to determine the initial sparse ones of the estimatedcrosstalk coefficients for one of a plurality of tones based onextrapolating or interpolating the improved sparse ones of the estimatedcrosstalk coefficients associated with other tones of the plurality oftones.

In some example embodiments, the other tones of the plurality of tonesare tones having a lower frequency than the one of the plurality oftones.

In some example embodiments, the one or more processors are configuredto estimate the estimated crosstalk values of significant ones of thedisturber lines by iteratively improving the estimated crosstalkcoefficients until a stop condition is satisfied.

In some example embodiments, the one or more processors are configuredto determine that the stop condition is satisfied when the estimatedcrosstalk coefficients for a current iteration is sufficiently close tothe estimated crosstalk coefficients for a previous iteration.

In some example embodiments, the one or more processors are configuredto obtain the pilot matrix such that columns of the pilot matrixrepresent columns of a Fourier matrix or Walsh-Hadamard Matrix.

One or more example embodiments relate to a non-transitory computerreadable medium storing instructions.

In some example embodiments, the instructions, when executed by one ormore processors, configure the one or more processors to, reducecrosstalk into a victim line from disturber lines in a communicationsystem by, obtaining a pilot matrix and a measurement vector associatedwith the pilot matrix, the pilot matrix representing pilot signalstransmitted by at least the disturber lines, the measurement vectorbeing influenced by the pilot signals via the crosstalk, estimatingestimated crosstalk coefficients of significant ones of the disturberlines by solving a reduced linear system using only non-clippedmeasurements in the measurement vector, the reduced linear system beingderived from the pilot matrix, determining compensation coefficients toreduce the crosstalk based on the estimated crosstalk coefficients, andreducing crosstalk by one or more of pre-compensating signalstransmitted on the victim line and post-compensating signals received onthe victim line based on the compensation coefficients.

One or more example embodiments relate to a method of estimatingcrosstalk into a victim line from disturber lines in a communicationsystem.

In some example embodiments, the method includes obtaining a pilotmatrix and a measurement vector associated with the pilot matrix, thepilot matrix representing pilot signals transmitted by at least thedisturber lines, the measurement vector being influenced by the pilotsignals via the crosstalk; and estimating estimated crosstalkcoefficients of significant ones of the disturber lines by solving areduced linear system using only non-clipped measurements in themeasurement vector, the reduced linear system being derived from thepilot matrix.

In some example embodiments, the method further includes displaying theestimated crosstalk coefficients to a user via a display device or animage forming apparatus.

BRIEF DESCRIPTION OF THE DRAWINGS

At least some example embodiments will become more fully understood fromthe detailed description provided below and the accompanying drawings,wherein like elements are represented by like reference numerals, whichare given by way of illustration only and thus are not limiting ofexample embodiments and wherein:

FIG. 1 illustrates a communication network according to some exampleembodiments;

FIG. 2 illustrates a method of initializing a joining line in acommunication system having a plurality of current active linesaccording to some example embodiments;

FIG. 3 illustrates a brute-force method of solving a reduced linearsystem to estimate cross talk values of only significant disturbersaccording to some example embodiments;

FIG. 4 illustrates an iterative method of solving a reduced linearsystem to estimate cross talk values of only significant disturbersaccording to some example embodiments; and

FIG. 5 illustrates a signal to noise ratio obtained on error feedbacktones with errors clipped to 1.0 and with various estimation methodsaccording to example embodiments.

DETAILED DESCRIPTION

Various example embodiments will now be described more fully withreference to the accompanying drawings in which some example embodimentsare shown.

Detailed illustrative example embodiments are disclosed herein. However,specific structural and functional details disclosed herein are merelyrepresentative for purposes of describing at least some exampleembodiments. Example embodiments may, however, be embodied in manyalternate forms and should not be construed as limited to only theembodiments set forth herein.

Accordingly, while example embodiments are capable of variousmodifications and alternative forms, embodiments thereof are shown byway of example in the drawings and will herein be described in detail.It should be understood, however, that there is no intent to limitexample embodiments to the particular forms disclosed, but on thecontrary, example embodiments are to cover all modifications,equivalents, and alternatives falling within the scope of exampleembodiments. Like numbers refer to like elements throughout thedescription of the figures. As used herein, the term “or” includes anyand all combinations of one or more of the associated listed items.

Although the terms first, second, etc. may be used herein to describevarious elements, these elements should not be limited by these terms.These terms are only used to distinguish one element from another. Forexample, a first element could be termed a second element, andsimilarly, a second element could be termed a first element, withoutdeparting from the scope of this disclosure. As used herein, the term“and/or,” includes any and all combinations of one or more of theassociated listed items.

When an element is referred to as being “connected,” or “coupled,” toanother element, it can be directly connected or coupled to the otherelement or intervening elements may be present. By contrast, when anelement is referred to as being “directly connected,” or “directlycoupled,” to another element, there are no intervening elements present.Other words used to describe the relationship between elements should beinterpreted in a like fashion (e.g., “between,” versus “directlybetween,” “adjacent,” versus “directly adjacent,” etc.).

The terminology used herein is for the purpose of describing particularexample embodiments only and is not intended to be limiting. As usedherein, the singular forms “a,” “an,” and “the,” are intended to includethe plural forms as well, unless the context clearly indicatesotherwise. It will be further understood that the terms “comprises,”“comprising,” “includes,” and/or “including,” when used herein, specifythe presence of stated features, integers, steps, operations, elements,and/or components, but do not preclude the presence or addition of oneor more other features, integers, steps, operations, elements,components, and/or groups thereof.

It should also be noted that in some alternative implementations, thefunctions/acts noted may occur out of the order noted in the figures.For example, two figures shown in succession may in fact be executedsubstantially concurrently or may sometimes be executed in the reverseorder, depending upon the functionality/acts involved.

Specific details are provided in the description to provide a thoroughunderstanding of example embodiments. However, it will be understood byone of ordinary skill in the art that example embodiments may bepracticed without these specific details. For example, systems may beshown in block diagrams so as not to obscure the example embodiments inunnecessary detail. In other instances, well-known processes, structuresand techniques may be shown without unnecessary detail in order to avoidobscuring example embodiments.

As discussed herein, illustrative embodiments are described withreference to acts and symbolic representations of operations (e.g., inthe form of flow charts, flow diagrams, data flow diagrams, structurediagrams, block diagrams, etc.) that may be implemented as programmodules or functional processes include routines, programs, objects,components, data structures, etc., that perform particular tasks orimplement particular abstract data types and may be implemented usingexisting hardware at, for example, existing endpoints, clients,gateways, nodes, agents, controllers, computers, cloud based servers,web servers, proxies or proxy servers, application servers, and thelike. As discussed later, such existing hardware may include, interalia, one or more Central Processing Units (CPUs), system-on-chip (SOC)devices, digital signal processors (DSPs),application-specific-integrated-circuits, field programmable gate arrays(FPGAs) computers or the like.

Although a flow chart or communication flow diagram may describe theoperations as a sequential process, many of the operations may beperformed in parallel, concurrently or simultaneously. In addition, theorder of the operations may be re-arranged. A process may be terminatedwhen its operations are completed, but may also have additional stepsnot included in the figure. A process may correspond to a method,function, procedure, subroutine, subprogram, etc. When a processcorresponds to a function, its termination may correspond to a return ofthe function to the calling function or the main function.

As disclosed herein, the term “storage medium”, “computer readablestorage medium” or “non-transitory computer readable storage medium” mayrepresent one or more devices for storing data, including read onlymemory (ROM), random access memory (RAM), magnetic RAM, core memory,magnetic disk storage mediums, optical storage mediums, flash memorydevices and/or other tangible machine readable mediums for storinginformation. The term “computer-readable medium” may include, but is notlimited to, portable or fixed storage devices, optical storage devices,and various other mediums capable of storing, containing or carryinginstruction(s) and/or data.

Furthermore, example embodiments may be implemented by hardware,software, firmware, middleware, microcode, hardware descriptionlanguages, or any combination thereof. When implemented in software,firmware, middleware or microcode, the program code or code segments toperform the necessary tasks may be stored in a machine or computerreadable medium such as a computer readable storage medium. Whenimplemented in software, a processor or processors will perform thenecessary tasks.

A code segment may represent a procedure, function, subprogram, program,routine, subroutine, module, software package, class, or any combinationof instructions, data structures or program statements. A code segmentmay be coupled to another code segment or a hardware circuit by passingand/or receiving information, data, arguments, parameters or memorycontents. Information, arguments, parameters, data, etc. may be passed,forwarded, or transmitted via any suitable means including memorysharing, message passing, token passing, network transmission, etc.

The terms “including” and/or “having”, as used herein, are defined ascomprising (i.e., open language). The term “coupled”, as used herein, isdefined as connected, although not necessarily directly, and notnecessarily mechanically. Terminology derived from the word “indicating”(e.g., “indicates” and “indication”) is intended to encompass all thevarious techniques available for communicating or referencing theobject/information being indicated. Some, but not all, examples oftechniques available for communicating or referencing theobject/information being indicated include the conveyance of theobject/information being indicated, the conveyance of an identifier ofthe object/information being indicated, the conveyance of informationused to generate the object/information being indicated, the conveyanceof some part or portion of the object/information being indicated, theconveyance of some derivation of the object/information being indicated,and the conveyance of some symbol representing the object/informationbeing indicated.

According to example embodiments, clients, gateways, nodes, agentscontrollers, computers, cloud based servers, web servers, applicationservers, proxies or proxy servers, and the like, may be (or include)hardware, firmware, hardware executing software or any combinationthereof. Such hardware may include one or more Central Processing Units(CPUs), system-on-chip (SOC) devices, digital signal processors (DSPs),application-specific-integrated-circuits (ASICs), field programmablegate arrays (FPGAs) computers or the like configured as special purposemachines to perform the functions described herein as well as any otherwell-known functions of these elements. In at least some cases, CPUs,SOCs, DSPs, ASICs and FPGAs may generally be referred to as processingcircuits, processors and/or microprocessors.

The endpoints, clients, gateways, nodes, agents, controllers, computers,cloud based servers, web servers, application servers, proxies or proxyservers, and the like, may also include various interfaces including oneor more transmitters/receivers connected to one or more antennas, acomputer readable medium, and (optionally) a display device. The one ormore interfaces may be configured to transmit/receive (wireline and/orwirelessly) data or control signals via respective data and controlplanes or interfaces to/from one or more network elements, such asswitches, gateways, termination nodes, controllers, servers, clients,and the like.

Benefits, other advantages, and solutions to problems will be describedabove with regard to specific embodiments of the invention. However, thebenefits, advantages, solutions to problems, and any element(s) that maycause or result in such benefits, advantages, or solutions, or causesuch benefits, advantages, or solutions to become more pronounced arenot to be construed as a critical, required, or essential feature orelement of any or all the claims.

The example embodiments may have different forms and/or be combined, andshould not be construed as being limited to the descriptions set forthherein.

FIG. 1 illustrates a communication system according to some exampleembodiment.

As shown in FIG. 1, a system 500 may include a distribution point oraccess node (AN) 100 and Customer Premises Equipment (CPEs) 200-1 to200-N, where N may be an integer greater than 1, the access node 100 andthe CPEs 200-1 to 200-N may be connected via respective communicationlines 300.

The access node 100 may be under control of an operator. The access node100 may include an optical network unit (ONU) 115, a network processor(NP) 120, processing devices 125-1 to 125-m, a controller 130, andanalog front ends (AFEs) 135-1 to 135-m, which may each include a linedriver (LD).

The ONU 115 may be configured to communicate with the network processor(NP) 120. The ONU 115 may provide a high-bandwidth data connection overa fiber optic channel to an optical line terminal (OLT) located in acentral office. The ONU 115 may pass received downstream data frames orpackets to the NP 120, and the NP 120 may determine the destination forthe frames or packets and accordingly forward the frames or packets toan appropriate interface (e.g., DSL, ADSL, VDSL, VDSL2, G.fast, etc.interface). Similarly, in the upstream direction, the NP 120 forwardsframes or packets from the interfaces to the ONU 115.

The NP 120 may provide signals to the processing devices 125-1 to 125-m.The processing devices 125 may be configured for point-to-pointcommunication.

Each of the processing devices 125 may communicate with a respective oneof the CPEs 200 over the communication lines 300 through an associatedone of the AFEs 135-1 to 135-m. The lines 300 (also referred to aslinks) may be telephone lines (e.g., twisted copper pairs), and the CPEs200-1 to 200-N may be modems or other interface devices operatingaccording to a communication standard for transmitting data overtelephone lines. The CPEs 200-1 to 200-N may be located in variouscustomer premises.

Each of the CPEs 200-1 to 200-N may include an AFE 255-1 to 255-m andrespective processing devices 260-1 to 260-m. Each of the AFEs 255-1 to255-m may be the same or substantially the same as the AFEs 135-1 to135-m.

The controller 130 may be configured to receive signal data collectivelyreferred to as a signal vector from the processing devices 125. Thesignal data may include signal values intended to be received bycorresponding ones of the processing devices 260-1 to 260-m in the CPEs200.

In the downstream direction, the controller 130 may also be configuredto precode the signal vector, and send the resulting data back to theprocessing devices 125 for transmission to the CPEs 200. The processingdevices 125 then send the precoded signal data over the respectivecommunication lines 300 via the respective AFEs 135-1 to 135-m.

In the upstream direction, the processing devices 125 receivecrosstalk-contaminated signals from the AFEs 135. The controller 130receives the crosstalk-contaminated signals (collectively referred to asreceived signal vector) from the processing devices 125, postcodes thereceived signal vector, and provides the processing devices 125 with thepost-compensated signal data. The processing devices 125 then continueto process the signal data to demodulate the intended upstreaminformation.

In vectored DSL systems, downstream crosstalk channel coefficients areestimated by the access node 100 sending pilot sequences downstream,measuring the received error at the CPE 200, and forwarding the receivederror samples back to the access node 100 for further processing. Theformat of the error samples may be standardized (G.vector), and mayinclude clipping of the measurements when outside of a specified range.In lines with strong crosstalk, and especially when using the higherfrequencies made available in the new VDSL2 35b profile, significantclipping can occur, leading to poor vectoring performance andsignificant loss of data rate. There may also be an analogous problem inupstream estimation, although this problem can be less constrained bystandardization since the error samples may be both measured andprocessed by the access node 100.

Generally, the data exchanged between processing devices would befrequency-domain samples, but alternatively the data could berepresented as time-domain samples, for example.

As discussed above, the controller 130 communicates with the processingdevices 125. Alternatively, the controller 130 may be between theprocessing devices 125 and the respective AFEs 135-1 to 135-M. Thus, thelocation of the controller 130 is not limited to the location shown inFIG. 1.

Furthermore, it will be understood that the access node 100 may includea memory, or multiple memories. The NP 120, the controller 130, and/orthe processing devices 125 may execute programs and/or program modulesstored on the memory to perform their respective functions and thefunctions of the access node 100. The operation of the access node 100will be described in greater detail below with respect to some exampleembodiments. The memories may be external to and/or internal to the NP120, the controller 130, and/or the AFEs 135. For the purposes ofsimplicity of illustration only, only a memory 140 associated with thecontroller 130 is shown.

The system 500 may utilize discrete multi-tone modulation (DMT). A DMTsystem uses a number of orthogonal subcarriers simultaneously.

Example embodiments take advantage of the geometry of a system. Morespecifically, because of the geometry of the system, the crosstalkexperienced by a joining line typically comes from only a portion of theactive lines already in the system.

When collecting larger and larger groups of twisted pair lines forvectoring, using twisted pair cable types commonly in use, the number oflines providing significant crosstalk into a particular line does notgrow without bound. Crosstalk may be considered significant if thecrosstalk causes a significant reduction in information carryingcapacity of the system, e.g., if the data rates, when a disturber lineis active, are less than the data rates when the disturber line isinactive, by more than a threshold percent. As an example, crosstalk maybe insignificant if it is lower in strength than other sources of noisein the system, such as thermal noise in receiver circuitry.

The lines providing crosstalk greater than a threshold (e.g.,significant crosstalk) may be referred to as significant disturberlines. The number of significant disturber lines is limited by geometricconsiderations, since typically the crosstalk strength is related to thephysical proximity in a binder, and only so many lines can be in closeproximity to each other.

As a result, in a large system, the crosstalk coupling vector g isexpected to be sparse, having a limited number of significant componentswhose positions in the crosstalk coupling vector g are not known apriori.

According to example embodiments, low frequency tones or historicinformation are used to identify the non-zero coefficients.

During an initialization process for the joining line, there may be N−1active lines, each of which is a potential disturber, such that afterinitialization, there are N active lines. As will be used throughout thedescription, the cross coupling vector g is a vector of length N andrepresents the channel coupling coefficients from each of the N linesinto the N-th line, respectively. To facilitate the description ofexample embodiments, the cross coupling vector g may be considered as anN×1 column vector.

The raw error feedback e[k] received on a victim line on tone k can bemodeled as:e[k]=PT[k]g[k]a  Eq. 1

In Eq. 1, P is the L×N pilot matrix, where L is the number of timeperiods and N is the number of active lines. T[k] is a diagonal N×Nmatrix with relative transmit gains on the diagonal, g[k] is an N-vectorof relative crosstalk coefficients, and a is the complex 4-QAMconstellation point having a real/imaginary value (1+j) on a 2D complexplane.

The raw error feedback e[k] may be processed using a clipping function ϕprior to sending the error feedback to the access node 100. Theprocessed error sample e^(c)[k] may then be expressed via Equation 2:e ^(c)[k]=ϕ(e[k])=ϕ(PT[k]g[k]a )  Eq. 2

In equation 2, ϕ is the clipping function (hard limiter in real andimaginary parts).

A conventional access node may estimate crosstalk by simply consideringe[k]=e^(c)[k], and by rearranging Equation 2 to obtain an estimatedchannel vector ĝ[k] of the channel vector g[k] using Equation 3:ĝ[k]=T[k]⁻¹(La)⁻¹ P ^(T) e ^(c)[k]  Eq. 3

In the absence of clipping, this conventional crosstalk estimation mayaccurately recover the crosstalk (ignoring noise), because the pilotsare orthogonal and satisfy P^(T)P=LI.

However, when the error samples are clipped, the clipping error isdefinable using Equation 4:δ[k]=e ^(c)[k]−e[k]=ϕ(PT[k]g[k]a)−PT[k]g[k]a  Eq. 4

The resulting deterministic error in the crosstalk vector may then beexpressed using Equation 5:ĝ[k]−g[k]=T[k]⁻¹(La)⁻¹ P ^(T)δ[k]  Eq. 5

As discussed below with reference to FIG. 2, in one or more exampleembodiments, rather than simply use the processed estimates of crosstalke^(c)[k] to estimate the crosstalk coupling vector g[k], the controller130 may, for each tone k, estimate the crosstalk coupling vector g[k]using only elements of the processed error vector e^(c)[k] that are notclipped (i.e., that are equal to corresponding elements of e[k]). Toreduce the number of unknown values of the crosstalk coupling vectorg[k] to be estimated, the controller 130 may only estimate elements ofthe crosstalk coupling vector g[k] corresponding to significantdisturbers, replacing other elements of the crosstalk coupling vectorg[k] with zero.

FIG. 2 illustrates a method of initializing a joining line in acommunication system having a plurality of current active linesaccording to some example embodiments.

Referring to FIGS. 1 and 2, for the purposes of description only, thisembodiment will be described with respect to implementation on thesystem of FIG. 1. For example, three lines associated with CPE 200-1 to200-3 in FIG. 1 may be considered current active lines and a fourth lineassociated with CPE 200-N may be a joining line.

While the example embodiments will be described with respect to ajoining line and a plurality of current active lines, exampleembodiments are not limited thereto. For example, a group of linessimultaneously join a vectored system such as the system 500 shown inFIG. 1, in which case the crosstalk from one or more of the joininglines on another one of the joining lines may also be estimated.Furthermore, crosstalk between current active lines may be estimatedusing error samples provided by the CPE associated with one or moreactive lines. Moreover, the crosstalk from the current active lines onanother line may be estimated, where the other line had previouslyjoined the system shown in FIG. 1, but has been in a power-savingoperation mode for a period of time and is now returning to normal-poweroperation mode. Accordingly, terms such as “joining line” and “at leasta first line” may refer to line(s) for which a crosstalk coupling vectoris to be determined and terms such as “a plurality of active lines” and“a plurality of second lines” may refer to lines from which thecrosstalk experienced by a joining line/at least a first line comesfrom.

The method may start by the controller 130 of the access node 100initializing an index of the tones k to an initial tone. In some exampleembodiments 130 the controller 130 may process tones k in the processedmeasurement vector e^(c)[k] from low tones to high tones and, therefore,the initial tone may be, for example, tone zero.

Thereafter, in operation S410, the controller 130 may obtain a pilotmatrix P having L×N dimensions with N columns of length L where thepilot matrix represents pilot signals transmitted by at least thedisturber lines, and transmit the pilot signals across the active linesbased on the obtained pilot matrix P.

For example, the controller 130 may generate the pilot matrix P bychoosing any L×N orthogonal matrix P, that is, any real matrix such thatthe product P ^(T) P is equal to a diagonal matrix S with positivediagonal entries. The pilot matrix P can then be obtained as a scaledversion of P, via the formula P=PS^(−1/2)√{square root over (L)}, whichensures that P^(T)P=LI.

In a system operating according to the G.vector standard, it is expectedthat each element of the matrix should be equal to +1 or −1. Such apilot matrix P can be obtained by taking a subset of N columns of an L×LWalsh-Hadamard matrix; methods for generating such matrices arewell-known to those skilled in the art.

The controller 130 may assign a different pilot sequence/column to eachof the N lines, where the sequence tells the line what pilot value tosend in each of the L time slots.

The controller 130 may provide the pilot matrix P to the processingdevices 125. The processing devices 125 then transmit pilot signals overthe plurality of subcarriers in accordance with sequence of pilotsidentified in the pilot matrix P.

In some example embodiment, the system 500 is a discrete multi-tonemodulation (DMT) system, which uses a number of orthogonal subcarrierssimultaneously. Accordingly, the processing devices 125 mayindependently and in parallel transmit pilot signals on each subcarrier,in accordance with the pilot matrix P. Therefore, the controller 130 mayprovide the pilot matrix P to the processing devices 125 and theprocessing devices 125 transmit pilot signals, over the plurality ofsubcarriers, across the plurality of current active lines as well as thejoining line in accordance with sequence of pilots identified in thepilot matrix P. In a typical DMT setting the processing device 125 forline n may receive the pilot value P[t,n] to be sent on line n at timet. The processing device may compute corresponding complex tone datau_(n)[t,k]=P[t,n] s_(n)[k] a, for each tone k=1, . . . K, where s_(n)[k]is a transmit scaling and a is the complex point (1+j). The tone datau_(n)[t,k] for a fixed value of t would be processed via IDFT and otherknown steps to obtain a time-domain DMT symbol for transmission.

In some example embodiments, the controller 130 may structure the pilotmatrix P in a way to facilitate low complexity matrix multiplicationwhen multiplying elements by the pilot matrix P. For example, thismultiplication can use the Fast Fourier Transform, if the columns of Pare selected from a Fourier matrix. Further, the multiplication can usethe Fast Hadamard Transform, if the controller 130 selects the columnsof P from a Walsh-Hadamard matrix. For example, a L×N pilot matrix P maybe obtained from an L×L Walsh-Hadamard matrix W, by concatenating N outof the L columns of W. The indices of the subset of columns chosen canbe denoted J. To apply the matrix P to a vector x of length N, a vectorx′ of length L is created. The elements of the vector x are insertedinto the elements of x′ indexed by the set J, and the remaining elementsof x′ are set to zero. Applying the Fast Hadamard Transform to thevector x′ may have the same effect as multiplying the vector x′ by W,which has the same effect as multiplying the vector a by P.

In operation S415, the controller 130 may advance the index of the tonesk to a next tone k+1.

In operation S420, the controller 130 may obtain the processedmeasurement vector e^(c)(k) for the joining line for the currentlyselected tone k in a set of subcarriers K. The processed measurementvector e^(c)(k) is a L×1 column vector that represents the error samplescomputed at a receiver of the CPE 200-n of the joining line during the Ltime instances such that the measurement vector e^(c)(k) is influencedby the pilot signals via the crosstalk, and which are obtained bynormalizing the values received at the receiver and subtracting theknown or estimated pilot value.

The processed measurement vector is modeled by Equation 6:e ^(c)(k)=M[k]g(k)+z(k)  Eq. 6where z(k) is a L×1 column vector representing measurement noiseassociated with the kth subcarrier, g[k] is a N×1 vector of normalizedcrosstalk coefficients to be estimated, where M[k] is the L×N matrixM[k]=PT[k] a, and where T[k] is an N×N diagonal matrix withT_(nn)[k]=s_(n)[k]/s_(N)[k].

In a system operating according to G. vector, the processed measurementvector e^(c)[k] may be obtained as error feedback from the joining lineN while sending pilot signals specified by the scaled pilot matrix M[k].

In operation S430, the controller 130 may determine whether any of theelements in the processed measurement vector e^(c)[k] were clipped, andmay proceed to operation S440 if clipped elements are present on tone k,or proceed to operation S460 if none of the elements of the measurementvector have experienced clipping on tone k.

For example, the controller 130 may assume that a real or imaginaryelement of received error feedback e^(c)[k] that is equal to a clippingthreshold has been clipped. The clipping threshold in use by aparticular CPE device 200 may be known to the controller 130 because itis specified in a standard recommendation, or specified by themanufacturer, or it may be inferred by the controller 130 based on thelargest error feedback value historically observed from that CPE device200. The controller 130 may assume that a received error feedbackcomponent e^(c) _(n)[k] for a tone k that is equal to a clippingthreshold is a measurement that has been clipped. Thus, it is assumedthat the access node 100 either knows or can estimate the clippingthreshold used on each CPE 200. In some example embodiments, thecontroller 130 may determine that the received error feedback e^(c)_(n)[k] for a tone k is clipped if the real or imaginary part of thereceived error feedback e^(c) _(n)[k] is perfectly equal to 1 or −1.However, example embodiments are not limited thereto.

In operation S440, if clipped elements are present on tone k, thecontroller 130 may determine which of the disturbers N are“insignificant,” and which are “significant.” For example, based on thecrosstalk estimates observed on previously processed tones withoutclipped error samples, the disturbers are divided into two groups:

-   -   Significant disturbers: with statistically significant non-zero        crosstalk.    -   Insignificant disturbers: disturbers with estimated crosstalk        consistent with the values expected from noise alone. To        estimate the level of noise in the system, the controller can        use correlation with a matrix Q orthogonal to the pilot matrix        P, as described below in conjunction with operation S460.

The controller may set corresponding crosstalk estimates g[k] to zerofor the insignificant disturbers.

In operation S450, the controller 130 may solve a reduced linear systemto estimate crosstalk values g[k] of only significant disturbers, usingonly non-clipped elements of the processed measurement vector e^(c)[k]as input.

As discussed below with reference to FIGS. 3 and 4, the controller 130may solve the reduced linear system using various methods including abrute-force method described with reference to FIG. 3 and an iterativemethod described with reference to FIG. 4.

In contrast, in operation S460, when the controller 130 determines thatnone of the elements in the processed measurement vector e^(c)[k] areclipped, the controller 130 may estimate the crosstalk vector g[k] withthe normal procedure using Eq. 3, discussed supra by correlating theprocessed measurement vector e^(c)[k] with the pilot matrix P, asrepresented by multiplication with the transposed pilot matrix P^(T).

In addition, the controller 130 may estimate the noise variance on tonek by correlating the processed measurement vector e^(c)[k] with a matrixQ that is orthogonal to the pilot matrix P, that is, if Q is a full rankL×M matrix, M≤L−N, such that Q^(T)P=0. Then for a tone k withoutclipping, the controller 130 may obtain the M×1 vector θ[k]=Q^(T)e^(c)[k] by correlating the processed measurement vector with Q. Due tothe orthogonality, the result is equal to θ[k]=Q^(T) z[k]. Assuming thatthe elements of the noise vector z[k] are independent, zero-mean sampleswith variance σ²[k], the controller 130 may estimate the noise varianceaffecting the error samples on tone k as

${{\hat{\sigma}}^{2}\lbrack k\rbrack} = {\frac{\sum\limits_{i = 1}^{M}\;{{\theta_{i}\lbrack k\rbrack}}^{2}}{\sum\limits_{i = 1}^{M}\;{\sum\limits_{n = 1}^{L}\;{Q_{ni}}^{2}}}.}$Knowing this variance, the controller 130 may estimate the expectedcontribution of noise to the result of Eq. 3, providing a means ofdistinguishing between significant disturbers (for example havingcrosstalk estimates above the level of typical noise-induced estimationerrors), and insignificant disturbers (having crosstalk estimates at orbelow the level of typical noise-induced estimation errors).

In operation S470, the controller 130 may determine whether the indexindicates that the tone k is the last of the tones K. For example, in aG.vector system the set of tones for which the CPEs provide errorsamples is configured by the VCE, and K would be the number of tones inthis set.

If the controller 130 determines that there are additional tones k toprocess, the controller 130 may proceed back to operation S415, advancethe index of the tones to k+1, and obtain the processed measurementvector e^(c)[k+1] for tone k+1. Alternatively, if the controller 130determines that the tone k is the last tone, the controller may proceedto operation S480.

In operation S480, the controller 130 may use the estimated crosstalkvalues to determine compensation coefficients to protect the joiningline associated with CPE 200-n from crosstalk from the active linesassociated with CPEs 200-1 to 200-3.

For example, the controller 130 may use pre-compensation for downstreamcommunication, and set the pre-compensation coefficients as follows:P _(Nj) =−g _(j), for eachj=1, . . . ,N−1  Eq. 7where j is an index applied for every line from 1 to N and C_(Nj) is thepre-compensation coefficient for protecting line N from crosstalk fromline j. The controller 130 may use post-compensation for upstreamcommunication, and set post-compensation coefficients as follows:C _(Nj) =−v _(j), for each j=1, . . . ,N−1where j is an index applied for every line from 1 to N and C_(Nj) is thepost-compensation coefficient for protecting line N from crosstalk fromline j, where v=g^(T)G_(N-1) ⁻¹ is a 1×N vector obtained by multiplyingthe estimated crosstalk coefficients g with the inverse of the(N−1)×(N−1) crosstalk matrix G_(N-1), where G_(N-1) represents thecrosstalk coefficients between all previously active lines, aspreviously estimated in conjunction with the activation of those lines.

In operation S490, to subsequent time periods, with respect tocommunication from the access node to the CPEs, the controller 130 mayuse the pre-compensation coefficients to pre-compensate the data signalstransmitted on the joining line N in order to reduce (or, alternatively,to eliminate) crosstalk into the line associated with CPE 200-N. Inparticular, tone data values are sent from all processing devices 125-1to 125-N to the controller 130, the controller 130 adds pre-compensationsignals to the signals based on the pre-compensation coefficients, andthe controller sends the pre-compensated signal to the correspondingprocessing device 125-N. In the cable 300, the crosstalk signals fromdisturber lines 1 through N−1 into victim line N are removed byinteracting with the pre-compensation signal transmitted on victim lineN.

Further, with respect to communication from the CPEs to the access node,the controller 130 may similarly define post-compensation coefficientsto post-compensate data signals received from the jointing line N toreduce (or, alternatively, to eliminate) crosstalk into the lineassociated with CPE 200-N. For example, received upstream tone datavalues may be sent from all processing devices 125-1 to 125-N to thecontroller 130. The controller 130 may determine post-compensated datasignals by forming linear combinations of the received tone data valuesaccording to the post-compensation coefficients, and the controller maysend the post-compensated signal to the corresponding processing device125-N. The post-compensation has the effect of reducing (or,alternatively, eliminating) the effects of crosstalk signals fromdisturber lines 1 through N−1 into victim line N that are present in thereceived tone data.

While example embodiments above describe an embodiment in which, afterthe controller 130 estimates crosstalk values g[k] of only significantdisturbers using only non-clipped elements of the processed measurementvector e^(c)[k] as input, the controller 130 uses, in operations S480and S490, the estimated crosstalk values to determine compensationcoefficients and reduces crosstalk based on the determined compensationcoefficients, example embodiments are not limited thereto. For example,in other example embodiments, after estimating crosstalk values g[k] ofonly significant disturbers using only non-clipped elements of theprocessed measurement vector e^(c)[k] as input, the controller 130 mayprovide the estimated crosstalk values to a technician or device forfurther processing without performing operations S480 and S490. Forexample, the estimated crosstalk values may be displayed on a displaydevice or printed via an image forming apparatus in a form that enablesa technician to evaluate the quality of one or more communication linesin the cable 300. Further, in other example embodiments, the controller130 may use the estimated crosstalk values g[k] to adjust transmit powerlevels on one or more communication lines in the cable 300 to affectbeneficial tradeoffs among data communication rates across thecommunication lines.

FIG. 3 illustrates a brute-force method of solving a reduced linearsystem to estimate cross talk values of only significant disturbersaccording to some example embodiments.

Referring to FIGS. 1 to 3, in operation S451A, the controller 130 maydetermine a reduced linear system by determining reduced pilot matricesP_(AS) and. P_(BS).

For example, the controller 130 determines a subset A of elements of theprocessed measurement vector e^(c)[k] such that the real component isnot clipped, and a subset B of elements of the processed measurementvector e^(c)[k] such that the imaginary component is not clipped. Fromoperation S440, the controller 130 may already have obtained a subset Sof lines whose crosstalk coefficients may be significant. The reducedpilot matrix P_(AS) is obtained from the pilot matrix P by removing allrows of P not in the set A, and all columns of P not in the set S, andthe reduced pilot matrix P_(BS) is similarly obtained from the sets Band S.

These reduced matrices define a reduced linear system e_(A)^(R)=P_(AS)y_(S) ^(R)+z_(A) ^(R) for the real measurement component anda reduced linear system e_(B) ^(I)=P_(BS)y_(S) ^(I)+z_(B) ^(I) for theimaginary measurement component. In this system, y_(S) ^(R) and y_(S)^(I) are the real and imaginary components, respectively, of themodulated crosstalk vector y_(S)=aT_(SS)g_(S), where g_(s) representsthe significant subset of the crosstalk vector g, and where T_(SS)represents the submatrix of T[k] including only rows and columns fromthe significant subset S.

Thereafter, in operation S452A, the controller 130 may solve a linearleast squares problem to obtain estimates of the modulated crosstalkvector components y_(S) ^(R) and y_(S) ^(I) from the measurements e_(A)^(R)=P_(AS)y_(S) ^(R)+z_(A) ^(R) and e_(B) ^(I)=P_(BS)y_(S) ^(I)+z_(B)^(I). For example, if P_(AS) and P_(BS) are of full rank, the controllermay multiply the measurements by pseudo-inverse matrices using thefollowing Equation:ŷ _(S) ^(R)=(P _(AS) ^(T) P _(AS))⁻¹ P _(AS) ^(T) e _(A) ^(R)ŷ _(S) ^(I)=(P _(BS) ^(T) P _(BS))⁻¹ P _(BS) ^(T) e _(B) ^(I)  Eq. 8

Other numerical methods of solving the linear least squares problemssuch as by QR decomposition or Cholesky decomposition known to thoseskilled in the art may alternatively be used.

In operation S453A, the controller 130 may estimate the significantelements of the crosstalk coupling vector by scaling the modulatedcrosstalk vector estimates as follows: ĝ_(S)=a⁻¹T_(SS) ⁻¹ (ŷ_(S)^(R)+jŷ_(S) ^(I)).

FIG. 4 illustrates an iterative method of solving a reduced linearsystem to estimate cross talk values of only significant disturbersaccording to some example embodiments.

Referring to FIGS. 1, 2 and 4, in operation S451B, the controller 130may determine initial sparse crosstalk estimates {tilde over (g)}[k,0]and may define an initial iteration variable to t=1.

In some example embodiments, the controller 130 may extrapolate theinitial crosstalk estimates for tone k from the final crosstalkestimates on other tones. For example, the controller 130 may predictthe expected crosstalk coefficient vector by linear extrapolation fromthe previous two tones, namely tone k−1 and tone k−2:{tilde over (g)} _(i)[k,0]=2{tilde over (g)} _(i)[k−1]−ĝ _(i)[k−2] if iis a significant disturber  Eq. 9

The indices, k, k−1, and k−2 refer to tones for which error samples areavailable. Therefore, if error samples are collected only on every 4thtone, each index k may be separated by four tones, such that tones 1004and 1000 are utilized when estimating crosstalk on tone 1008.

While linear interpolation may introduce some error into the crosstalkestimate {tilde over (g)}[k,0], the controller 130 may reduce this errorin each iteration.

In operation S452B, the controller 130 may apply the pilot matrix P tothe sparse crosstalk estimates {tilde over (g)}[k] and perform scalingto obtain the predicted error feedback:{tilde over (e)}[k]=PT[k]{tilde over (g)}[k]a  Eq. 10

As discussed above with reference to operation S410, computationalcomplexity of this operation may be reduced when the pilot matrix P isstructured in a way to facilitate low complexity matrix multiplicationwhen multiplying elements by the pilot matrix P. For example, thismultiplication can use the Fast Fourier Transform, if the columns of Pare from a Fourier matrix, or the Fast Hadamard Transform, if thecolumns of P are from a Walsh-Hadamard matrix.

In operation S453B, the controller may overwrite clipped values in theprocessed measurement values e^(c)[k] with corresponding predictedmeasurement values {tilde over (e)}[k] to obtain corrected measurementvalues ê[k], and maintain unclipped measurement values without anyoverwriting as follows:ê _(n) ^(R)[k]={tilde over (e)} _(n) ^(R)[k], if |e _(n) ^(c,R)[k]| isat clipping thresholdê _(n) ^(R)[k]=e _(n) ^(c,R)[k], if |e _(n) ^(c,R)[k]| is below clippingthresholdê _(n) ^(I)[k]={tilde over (e)} _(n) ^(I)[k], if |e _(n) ^(c,I)[k]| isat clipping thresholdê _(n) ^(I)[k]=e _(n) ^(c,I)[k], if |e _(n) ^(c,I)[k]| is below clippingthreshold  Eq. 10

In Eq. 10, the superscripts R and I may refer to real and imaginarycomponents, respectively.

In operation S454B, the controller 130 may compute the estimated densecrosstalk vector g[k] from the corrected error samples ê[k] bymultiplying the corrected error samples by a pilot matrix transposeP^(T) and then scaling, using the following equation:g [k]=T[k]⁻¹(La)⁻¹ P ^(T) ê[k]  Eq. 12

As discussed above, again computational complexity may be reduced whenthe pilot matrix P, and thus the pilot matrix transpose P^(T), isstructured in a way to facilitate low complexity matrix multiplicationwhen multiplying elements by the pilot matrix transpose P^(T).

In operation S455B, the controller 130 may overwrite dense crosstalkestimates associated with the insignificant disturbers with zero toobtain improved sparse crosstalk estimates {tilde over (g)}[k,t] fortone k associated with iteration t as follows:{tilde over (g)} _(i)[k,t]= g _(i)[k] if i is a significant disturber{tilde over (g)} _(i)[k,t]=0, if i is not a significant disturber  Eq.13

As discussed above, linear interpolation may introduce some error intothe initial crosstalk estimate {tilde over (g)}[k,0], and some of thiserror may propagate into the dense estimate g[k]. However, thecontroller 130 may further reduce this error by setting insignificantdisturbers to exactly zero.

In operation S456B, the controller 130 may determine whether a stopcondition is satisfied. In some example embodiments the stop conditionmay be a maximum number of iterations, or crosstalk estimate {tilde over(g)}[k,t] for the current iteration t being substantially the same asthe crosstalk estimate {tilde over (g)}[k,t−1] for the previousiteration t−1.

If the stop condition is satisfied, the controller 130 may complete theiterative solving of the reduced linear system, determine the finalcrosstalk estimate on tone k to be the latest sparse estimateĝ[k]={tilde over (g)}[k,t], and proceed to operation S480.

If the stop condition is not satisfied, the controller 130 may proceedto operation S457B and advance the index of iterations such that t=t+1,and proceed back to operation S452B to repeat operations S452B to S456Bmultiple times on a given tone k to further improve the accuracy of thecrosstalk estimate {tilde over (g)}[k,t].

FIG. 5 illustrates a signal to noise ratio obtained on error feedbacktones with errors clipped and with various estimation methods accordingto example embodiments.

Referring to FIG. 5, FIG. 5 illustrates the signal to noise ratio (SNR)obtained on tones of different frequencies by an example joining line,when different methods of crosstalk channel estimation are used. The SNRvalues are generated from a simulation of these estimation procedures,using channel information representative of a 50-pair twisted pair cableof length 300 m, including 1 joining line and N−1=34 active lines. Inthis simulation, the clipping threshold for normalized error feedbackwas assumed to be 2.0.

In FIG. 5, the dotted curve indicates the SNR obtained if no estimationor precoding is performed. The dash-dot curve indicates the SNR obtainedwith perfect estimation, fully removing all crosstalk. The dashed curveindicates the SNR obtained using a conventional estimation proceduredescribed by Eq. 3, in which the possible clipping of error samples isignored. Finally, the solid curve indicates the SNR obtained accordingto some example embodiments as described by FIG. 4, where in operationS451B, the initial sparse crosstalk estimates are obtained via Eq. 9,and where the stopping condition is such that operations S452B throughS455B are executed once for each tone having clipped measurements.

As illustrated, the proposed estimation method provides a higher SNRthan the conventional method over a range of frequencies. As a result,the proposed estimation method may allow communication at a higher datarate than could be obtained with the conventional method.

Example embodiments being thus described, it will be obvious that thesame may be varied in many ways. Such variations are not to be regardedas a departure from the spirit and scope of example embodiments, and allsuch modifications as would be obvious to one skilled in the art areintended to be included within the scope of the claims.

I claim:
 1. A method of reducing crosstalk into a victim line fromdisturber lines in a communication system, the method comprising:obtaining a pilot matrix and a measurement vector associated with thepilot matrix, the pilot matrix representing pilot signals transmitted byat least the disturber lines, the measurement vector being influenced bythe pilot signals via the crosstalk; estimating crosstalk coefficientsof significant ones of the disturber lines by solving a reduced linearsystem using only non-clipped measurements in the measurement vector,the reduced linear system being derived from the pilot matrix;determining compensation coefficients to reduce the crosstalk based onthe crosstalk coefficients; and reducing crosstalk by one or more ofpre-compensating signals transmitted on the victim line andpost-compensating signals received on the victim line based on thecompensation coefficients.
 2. The method of claim 1, further comprising:determining which elements of the measurement vector are clippedmeasurements and which of the elements are the non-clipped measurements;and determining which of the disturber lines are insignificant disturberlines and significant disturber lines, wherein the estimating includessetting the crosstalk coefficients associated with the insignificantdisturber lines to zero.
 3. The method of claim 2, wherein theestimating comprises: determining reduced pilot matrices; and estimatingthe crosstalk coefficients by solving a least squares problem based onthe reduced pilot matrices.
 4. The method of claim 3, wherein thesolving the least squares problem comprises: computing pseudo-inversematrices; and multiplying the non-clipped measurements by thepseudo-inverse matrices to estimate the crosstalk coefficients.
 5. Themethod of claim 2, wherein the estimating comprises: applying the pilotmatrix to initial sparse ones of the crosstalk coefficients to generatepredicted measurement values; overwriting clipped measurement valueswith the predicted measurement values to generate corrected measurementvalues; multiplying the corrected measurement values by a transpose ofthe pilot matrix to generate dense ones of the crosstalk coefficients;and overwriting ones of the dense ones of the crosstalk coefficientsassociated with the insignificant disturber lines to zero to obtainimproved sparse ones of the crosstalk coefficients.
 6. The method ofclaim 5, further comprising: determining the initial sparse ones of thecrosstalk coefficients for one of a plurality of tones based onextrapolating or interpolating the improved sparse ones of the crosstalkcoefficients associated with other tones of the plurality of tones. 7.The method of claim 6, wherein the other tones of the plurality of tonesare tones having a lower frequency than the one of the plurality oftones.
 8. The method of claim 4, wherein the estimating comprises:iteratively improving the crosstalk coefficients until a stop conditionis satisfied.
 9. The method of claim 8, wherein the estimating includesdetermining that the stop condition is satisfied when the crosstalkcoefficients for a current iteration is sufficiently close to thecrosstalk coefficients for a previous iteration.
 10. The method of claim1, wherein the obtaining includes obtaining the pilot matrix such thatcolumns of the pilot matrix represent columns of a Fourier matrix orWalsh-Hadamard Matrix.
 11. A device comprising: one or more processorsconfigured to reduce crosstalk into a victim line from disturber linesin a communication system by, obtaining a pilot matrix and a measurementvector associated with the pilot matrix, the pilot matrix representingpilot signals transmitted by at least the disturber lines, themeasurement vector being influenced by the pilot signals via thecrosstalk, estimating crosstalk coefficients of significant ones of thedisturber lines by solving a reduced linear system using onlynon-clipped measurements in the measurement vector, the reduced linearsystem being derived from the pilot matrix, determining compensationcoefficients to reduce the crosstalk based on the crosstalkcoefficients, and reducing crosstalk by one or more of pre-compensatingsignals transmitted on the victim line and post-compensating signalsreceived on the victim line based on the compensation coefficients. 12.The device of claim 11, wherein the one or more processors are furtherconfigured to, determine which elements of the measurement vector areclipped measurements and which of the elements are the non-clippedmeasurements; and determine which of the disturber lines areinsignificant disturber lines and significant disturber lines, whereinthe one or more processors are configured to estimate the crosstalkcoefficients of significant ones of the disturber lines by setting thecrosstalk coefficients associated with the insignificant disturber linesto zero.
 13. The device of claim 12, wherein the one or more processorsare configured to estimate the crosstalk values of significant ones ofthe disturber lines by, determining reduced pilot matrices; andestimating the crosstalk coefficients by solving a least squares problembased on the reduced pilot matrices.
 14. The device of claim 12, whereinthe one or more processors are configured to estimate the crosstalkvalues of significant ones of the disturber lines by, applying the pilotmatrix to initial sparse ones of the crosstalk coefficients to generatepredicted measurement values; overwriting clipped measurement valueswith the predicted measurement values to generate corrected measurementvalues; multiplying the corrected measurement values by a transpose ofthe pilot matrix to generate dense ones of the crosstalk coefficients;and overwriting ones of the dense ones of the crosstalk coefficientsassociated with the insignificant disturber lines to zero to obtainimproved sparse ones of the crosstalk coefficients.
 15. The device ofclaim 14, wherein the one or more processors are further configured to,determine the initial sparse ones of the crosstalk coefficients for oneof a plurality of tones based on extrapolating or interpolating theimproved sparse ones of the crosstalk coefficients associated with othertones of the plurality of tones.
 16. The device of claim 15, wherein theother tones of the plurality of tones are tones having a lower frequencythan the one of the plurality of tones.
 17. The device of claim 14,wherein the one or more processors are configured to estimate thecrosstalk values of significant ones of the disturber lines by,iteratively improving the crosstalk coefficients until a stop conditionis satisfied.
 18. The device of claim 17, wherein the one or moreprocessors are configured to determine that the stop condition issatisfied when the crosstalk coefficients for a current iteration issufficiently close to the crosstalk coefficients for a previousiteration.
 19. The device of claim 11, wherein the one or moreprocessors are configured to obtain the pilot matrix such that columnsof the pilot matrix represent columns of a Fourier matrix orWalsh-Hadamard Matrix.
 20. A method of estimating crosstalk into avictim line from disturber lines in a communication system, the methodcomprising: obtaining a pilot matrix and a measurement vector associatedwith the pilot matrix, the pilot matrix representing pilot signalstransmitted by at least the disturber lines, the measurement vectorbeing influenced by the pilot signals via the crosstalk; and estimatingcrosstalk coefficients of significant ones of the disturber lines bysolving a reduced linear system using only non-clipped measurements inthe measurement vector, the reduced linear system being derived from thepilot matrix.